Integration of variable renewables such as solar and wind has grown at an unprecedented pace in Europe over the past two decades. As the share of solar and wind rises, it becomes increasingly important for long-term energy system models to adequately represent their short-term variability. This paper uses a long-term TIMES model of the European power and district heat sectors towards 2050 to explore how stochastic modelling of short-term solar and wind variability as well as different temporal resolutions influence the model performance. Using a stochastic model with 48 time-slices as benchmark, the results show that deterministic models with low temporal resolution give a 15–20% underestimation of annual costs, an overestimation of the contribution of variable renewables (13–15% of total electricity generation) and a lack of system flexibility. The results of the deterministic models converge towards the stochastic solution when the temporal resolution is increased, but even with 2016 time-slices, the need for flexibility is underestimated. In addition, the deterministic model with 2016 time-slices takes 30 times longer to solve than the stochastic model with 48 time-slices. Based on these findings, a stochastic approach is recommended for long-term studies of energy systems with large shares of variable renewable energy sources. © 2020 The Authors